The solutions of interest will be sourced by normal matter in the form of a relativistic thermal gas with \(T^\mu _\mu =0\) , i.e. \(\rho =3p\) . Past work [1]}, [2]} on these solutions has used field equations for the metric functions \(A(r)\)  and \(B(r)\)  based on the line element

ds2=-B(r)dt2+A(r)dx2+r2 d2+r2 ()2 d2
.
The choice of this metric has a distinct advantage for numerical work, namely that the field equations are independent of the overall scale of \(B(r)\) . This eliminates one parameter, since the overall scale of \(B(r)\)  can simply be fixed from the boundary condition \(B(\infty )=1\) . In addition the field equations can be reduced to contain no more than second derivatives of \(A(r)\)  and \(B(r)\)  [3]}.
